Alright, well, I've read over your "demand for rail transport" post and .pdf several times, and I actually have a few questions (in no particular order):

1) Why would you assume that the percentage of people that take a train is a square-root of the population?

2) For your "Preference (Based on population)", why would you divide the square-roots? For Cork to Dublin you have 345/711 = 0.49, but for Dublin to Cork you also have .49; which, by your own function, would be wrong. Dublin to Cork would be 711/345 = 2.06. Therefore, I'm curious as to the reasoning behind this.

3) The "Demand Value (b)" calculations need to shown as to how you derived them.

4) In the "Demand Difference (a-b)", you have negative demand, which doesn't make any sense. Does that mean that people are willing to pay more money to not travel by rail?

Anyway, I have my own theory as towards a railway demand function, but I'd by more than willing to modify it after I read your reply for my questions.

Thanks.